Question

what is the value of the y - coordinate of the solution to the system of equations 2x + y = 8 and x - 3y = - 3
3
2

• 2
• 3

5 multiple choice 2 points
what is the solution of the system of equations 2x - 5y = 11 and - 2x + 3y = - 9?
(-1, 3)
(-3, -1)
(3, -1)
(3, 1)
6 multiple choice 2 points
what is the solution of the system of equations below?
2x + 3y = 7
x + y = 3
(4, -1)
(4, 1)
(1, 2)
(2, 1)

Explanation:

Problem 1:

Step1: Isolate x from second equation

$x = 3y - 3$

Step2: Substitute into first equation

$2(3y - 3) + y = 8$

Step3: Simplify and solve for y

$6y - 6 + y = 8 \implies 7y = 14 \implies y=2$

Problem 2:

Step1: Add the two equations

$(2x - 5y) + (-2x + 3y) = 11 + (-9)$

Step2: Solve for y

$-2y = 2 \implies y = -1$

Step3: Substitute y into first equation

$2x - 5(-1) = 11 \implies 2x = 6 \implies x=-3$

Problem 3:

Step1: Isolate x from second equation

$x = 3 - y$

Step2: Substitute into first equation

$2(3 - y) + 3y = 7$

Step3: Simplify and solve for y

$6 - 2y + 3y = 7 \implies y=1$

Step4: Solve for x

$x = 3 - 1 = 2$

Answer:

1. 2
2. (-3, -1)
3. (2, 1)